let $\mathrm{M}\in\lbrace0,1\rbrace^n$ be the adjacency matrix of a graph $\mathrm{G}\left(V,E\subseteq\lbrace\lbrace u,v\rbrace| u,v\in V\rbrace\right)$ of order $n$.

>**Question:**
is it true that $$\mathrm{rank}(\mathrm{M})=\max_{n'}\mathrm{K}_{n'}\subseteq\mathrm{G}$$
resp. how is the the rank of the adjacency matrix related to the size of the maximal clique?